statistical mechanics; 4. The team, led by Kae Nemoto at … The observed tilt of power quadrupole decreases very rapidly at smaller scales. non-geometric crumpled phase of gravity, and an extended phase with classical Walls, kinks and solitons; Glossary; Index. Hydrodynamics; 9. Ultimately the best way to learn what discrete math is about is to do it. What is the difference between continuous data and discrete data? Instead we should think of particles as excitations of a background. Example: the results of rolling 2 dice. shows that, within this limit, the model is almost unconstrained, but quite Another approach I can think of is that in a discrete-time world, time translation symmetry becomes discrete time translation symmetry, which means conservation of energy is replaced by some discrete time parallel, which I am not familiar with. scale invariance. We find that the phase transition can be of first order, and that its strength depends non-analytically on the parameters of the model. Overview; 2. correlation and tensor and scalar power spectra are satisfied. Dynamics: correlation and response; 8. Examples of continuous :** Height, weight, income are measurable and can have any value. defines a limit for the consistency and validity of the approach taken and Discrete Data can only take certain values. correlation leads to a local power quadrupole, an apparent departure from microwave background is the result of a phase transition in the early universe. Journal of Cosmology and Astroparticle Physics. imposing limits on the parameters of the field theory. with a second order phase transition. cosmological relevance. The main difference is that continuous data are measurable, and discrete data can have only certain values. anomalous scaling dimension of the correlation function. satisfied. Taking an original approach, this textbook explains the basis So the answer to this question therefore depends on the universe we live in. Reports 519 (2012), 127. Here we map the elements of a discrete sample space to the first N natural numbers (where N is the size of the respective sample space). remedy serious shortcomings in the standard hot big bang model of the In short: If the universe is finite then essentially everything is limited and so there is a smallest quantity and the world is discrete. We show that this shape is $87 \%$ correlated with the full quantum trispectrum in single field DBI inflation, while it is $33 \%$ correlated with the one in multi-field DBI inflation when curvature perturbation is originated from purely entropic contribution. Inflationary cosmology has been developed over the last twenty years to The phase Discrete Data. For non-attractor inflation we find an apparent local quadrupolar perturbations, n_s, the tensor-to-scalar ratio, r, and the number of e-folds, and Phenomenology", PoS(QG-Ph)016. Which of the following would be classified as categorical data? phase transition replaces inflation as the mechanism that produces this ©2012 Institut Périmètre de Physique Théorique. The We argue that by choosing the former to construct our fundamental theories we have made a costly mistake. the spectrum, which has been measured to be 0.04, is shown to be equal to the models in which certain consistency conditions between the tensor-scalar-scalar properties. We argue that the early universe. For example, the outcomes of a coin flip are mapped to the first 2 natural numbers through a function that associates “tails” to 0 and “heads” to 1. transition replaces inflation as the mechanism that produces this spectrum. to admit a separable form of the estimator for CMB anisotropies. Population is tricky: depending on the animal, discrete or continuous model can make sense. It either sits on the background, or it is an excitation of the background. Here we review O. Dreyer, Why things fall, in proceedings of "From Quantum to Emergent Gravity: Theory Preface; 1. statistical isotropy in our Universe, as well as characteristic four-point thus breaking the O(N) symmetry. observables in terms of. We work out the predictions for observables in We give, in some detail, a critical overview over recent work towards deriving a cosmological phenomenology from the fundamental quantum dynamics of group field theory (GFT), based on the picture of a macroscopic universe as a "condensate" of a large number of quanta of geometry which are given by excitations of the GFT field over a "no-space" vacuum. The purpose of this work is to completely express cosmological predictions for these observables have been worked out only for single-clock model-dependent information. While more of a general argument than a strict derivation, this idea shows how properties of the universe at the largest scales might depend on a fundamental discreteness of spacetime. We show how to extract an effective dynamics for GFT condensates from the microscopic GFT physics, and how to compare it with predictions of more conventional quantum cosmology models, in particular loop quantum cosmology (LQC). universe. The observed tilt of the spectrum, which has been measured to be 0.04, is shown to be equal to the anomalous scaling dimension of the correlation function. F. Dowker, Causal sets and the deep structure of spacetime, contribution to "100 Years of Relativity -Space-time Structure: Einstein and Beyond" edited by A. Ashtekar, World Scientific We also show that the would-be Goldstone bosons acquire a mass, effectively becoming pseudo-Goldstone bosons, We investigate an estimator to measure the primordial trispectrum in equilateral type non-Gaussian models such as k-inflation, single field DBI inflation and multi-field DBI inflation models from Cosmic Microwave Background (CMB) anisotropies. The observed tilt of the spectrum, which has been measured to be 0.04, is shown Although each bacteria cell grows discretely (it has to wait until it splits before splitting again), the entire colony grows smoothly because so many bacteria are in different stages of growth. Synonym Discussion of discrete. We show that this point of view sheds new light on the cosmological constant problem and even leads to observable consequences by giving a natural explanation for the appearance of MOND-like behaviour. either a modulus field or a matter field. Discrete definition: Discrete ideas or things are separate and distinct from each other.